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TMF, 2011, Volume 167, Number 2, Pages 311–322 (Mi tmf6642)  

This article is cited in 3 scientific papers (total in 3 papers)

Nonuniqueness of a Gibbs measure for a model on the Cayley tree

U. A. Rozikov, G. T. Madgoziev

Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, Tashkent, Uzbekistan

Abstract: We propose a model on the Cayley tree and prove that a uncountable set of $\widehat G$-periodic Gibbs measures exists for this model, in contrast to models studied previously.

Keywords: Cayley tree, configuration, hard-core model, Gibbs measure

DOI: https://doi.org/10.4213/tmf6642

Full text: PDF file (434 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2011, 167:2, 668–679

Bibliographic databases:

Received: 11.10.2010
Revised: 29.11.2010

Citation: U. A. Rozikov, G. T. Madgoziev, “Nonuniqueness of a Gibbs measure for a model on the Cayley tree”, TMF, 167:2 (2011), 311–322; Theoret. and Math. Phys., 167:2 (2011), 668–679

Citation in format AMSBIB
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\by U.~A.~Rozikov, G.~T.~Madgoziev
\paper Nonuniqueness of a~Gibbs measure for a~model on the~Cayley tree
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\vol 167
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\pages 311--322
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\transl
\jour Theoret. and Math. Phys.
\yr 2011
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\issue 2
\pages 668--679
\crossref{https://doi.org/10.1007/s11232-011-0051-9}
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  • https://doi.org/10.4213/tmf6642
  • http://mi.mathnet.ru/eng/tmf/v167/i2/p311

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus
    2. N. M. Khatamov, “Nonuniqueness of a Gibbs measure for the Ising ball model”, Theoret. and Math. Phys., 180:3 (2014), 1030–1039  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. N. M. Khatamov, G. T. Madgoziev, “Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree”, Theoret. and Math. Phys., 183:3 (2015), 836–845  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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